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Bayesian inference for spatio-temporal spike-and-slab priors [article]

Michael Riis Andersen, Aki Vehtari, Ole Winther, Lars Kai Hansen
2017 arXiv   pre-print
We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab  ...  An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow.  ...  Figures 16(g)-(h) show the same plots for the signal x 2 . Bayesian Inference for Spatio-temporal Spike-and-Slab Priors . We used the SPM8 software (Ashburner et al., 2010) . .  ... 
arXiv:1509.04752v3 fatcat:hssscrspp5hu3pprd2jeet7t6a

Spatio-Temporal Structured Sparse Regression With Hierarchical Gaussian Process Priors

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova
2018 IEEE Transactions on Signal Processing  
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference.  ...  It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and one-level Gaussian process  ...  For spike and slab priors a spatio-temporal structure is modelled with a one-level Gaussian processes prior [25] , where the prior is imposed on all locations of non-zero components together.  ... 
doi:10.1109/tsp.2018.2858207 fatcat:6mc6ps35krbwrghxr2ptpqk3aq

Structured Sparse Modelling with Hierarchical GP [article]

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova
2017 arXiv   pre-print
It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients.  ...  In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed.  ...  One of the Bayesian approaches to force the coefficients being zeros is the spike and slab prior [3] : each component is modelled as a mixture of spike, that is the delta-function in zero, and slab, that  ... 
arXiv:1704.08727v1 fatcat:abjcxoqutrak3d44w6mj5chrvy

Spatio-temporal Spike and Slab Priors for Multiple Measurement Vector Problems [article]

Michael Riis Andersen, Ole Winther, Lars Kai Hansen
2015 arXiv   pre-print
We propose a probabilistic model that takes this structure into account by generalizing the structured spike and slab prior and the associated Expectation Propagation inference scheme.  ...  We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (  ...  CONCLUSION & OUTLOOK We extended the structured spike and slab prior and the associated Expectation Propagation inference scheme to cope with smooth temporal evolution of the sparsity pattern.  ... 
arXiv:1508.04556v1 fatcat:nrpvdi65dzcbfhlwvjoub6uuji

NPBayes-fMRI: Non-parametric Bayesian General Linear Models for Single- and Multi-Subject fMRI Data

Jeong Hwan Kook, Michele Guindani, Linlin Zhang, Marina Vannucci
2017 Statistics in Biosciences  
The modeling approach is based on a spatio-temporal linear regression model that specifically accounts for the between-subjects heterogeneity in neuronal activity via a spatially informed multi-subject  ...  non-parametric variable selection prior.  ...  A spiked non-parametric prior is imposed on the coefficients β iν j , i.e., a spike-and-slab prior where the slab distribution is modeled as a non-parametric prior, as β iν j |γ iν j , G i ∼ γ iν j G i  ... 
doi:10.1007/s12561-017-9205-0 fatcat:dgd74eetmjee3hlcco5lcllisi

Bayesian uncertainty quantification for data-driven equation learning [article]

Simon Martina-Perez, Matthew J. Simpson, Ruth E. Baker
2021 arXiv   pre-print
Equation learning aims to infer differential equation models from data.  ...  We generate noisy data using a stochastic agent-based model and combine equation learning methods with approximate Bayesian computation (ABC) to show that the correct differential equation model can be  ...  Acknowledgements: The authors would like to thank the referees for their comments.  ... 
arXiv:2102.11629v4 fatcat:dpcuqkqmobeghcix5onvcnogfe

Quantifying the Economic Impact of Extreme Shocks on Businesses using Human Mobility Data: a Bayesian Causal Inference Approach [article]

Takahiro Yabe, Yunchang Zhang, Satish Ukkusuri
2020 arXiv   pre-print
However, surveys often suffer from high cost and long time for implementation, spatio-temporal sparsity in observations, and limitations in scalability.  ...  Recently, large scale human mobility data (e.g. mobile phone GPS) have been used to observe and analyze human mobility patterns in an unprecedented spatio-temporal granularity and scale.  ...  The work of T.Y. and S. V.  ... 
arXiv:2004.11121v1 fatcat:b7ry3uhdtzf3rldmeu5ntxpv3q

Bayesian statistics and modelling

Rens van de Schoot, Sarah Depaoli, Ruth King, Bianca Kramer, Kaspar Märtens, Mahlet G. Tadesse, Marina Vannucci, Andrew Gelman, Duco Veen, Joukje Willemsen, Christopher Yau
2021 Nature Reviews Methods Primers  
This Primer describes the stages involved in Bayesian analysis, from specifying the prior and data models to deriving inference, model checking and refinement.  ...  We discuss the importance of prior and posterior predictive checking, selecting a proper technique for sampling from a posterior distribution, variational inference and variable selection.  ...  Spike-and-slab variable selection priors that incorporate structural information on the brain have been investigated within a wide class of spatio-temporal hierarchical models for the detection of activation  ... 
doi:10.1038/s43586-020-00001-2 fatcat:ezphge7kzzdwbmg37t3em7s7ui

Quantifying the economic impact of disasters on businesses using human mobility data: a Bayesian causal inference approach

Takahiro Yabe, Yunchang Zhang, Satish V. Ukkusuri
2020 EPJ Data Science  
However, surveys often suffer from high cost and long time for implementation, spatio-temporal sparsity in observations, and limitations in scalability.  ...  Recently, large scale human mobility data (e.g. mobile phone GPS) have been used to observe and analyze human mobility patterns in an unprecedented spatio-temporal granularity and scale.  ...  Acknowledgements We thank Safegraph for preparing the mobile phone GPS data used in this study.  ... 
doi:10.1140/epjds/s13688-020-00255-6 fatcat:t6cjbbcuorbcfpstg7ws22a564

A Bayesian Variable Selection Approach Yields Improved Detection of Brain Activation From Complex-Valued fMRI

Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel Rowe
2018 Journal of the American Statistical Association  
We develop models with complexvalued spike-and-slab priors on the activation parameters that are able to combine the magnitude and phase information.  ...  We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data.  ...  Adding spatio-temporal structure that can better describe the data could potentially lead to further improved results, but would also lead to more computationally intensive models that may be not be feasible  ... 
doi:10.1080/01621459.2018.1476244 fatcat:zj5pjupy7ngcjjqu5cu7e2v7de

A Truncated EM Approach for Spike-and-Slab Sparse Coding [article]

Abdul-Saboor Sheikh, Jacquelyn A. Shelton, Jörg Lücke
2014 arXiv   pre-print
We study inference and learning based on a sparse coding model with 'spike-and-slab' prior.  ...  In applications to source separation we find that both approaches improve the state-of-the-art in a number of standard benchmarks, which argues for the use of 'spike-and-slab' priors for the corresponding  ...  Acknowledgements Furthermore, we acknowledge support by the Frankfurt Center for Scientific Computing (CSC Frankfurt).  ... 
arXiv:1211.3589v3 fatcat:oa6bkopd4faeph6z77pgpga6ya

Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions [article]

Arno Solin, Pasi Jylänki, Jaakko Kauramäki, Tom Heskes, Marcel A. J. van Gerven, Simo Särkkä
2016 arXiv   pre-print
We apply the method to both simulated and empirical data, and demonstrate the efficiency and generality of our Bayesian source reconstruction approach which subsumes various classical approaches in the  ...  the number of time steps, m is the number of sources, and n is the number of sensors.  ...  Acknowledgements This work was supported by the Academy of Finland grant numbers 266940 and 273475, the Netherlands Organization for Scientific Research (NWO) grant numbers 612.001.211 and 639.072.513,  ... 
arXiv:1604.04931v1 fatcat:zfssqpcu35cxjgrvvv7nsxd5rq

Spatio-Temporal Patterns in Portuguese Regional Fertility Rates: A Bayesian Approach for Spatial Clustering of Curves

Zhen Zhang, Arnab Bhattacharjee, João Marques, Tapabrata Maiti
2021 Journal of Official Statistics  
Here, we consider Bayesian hierarchical models with separable spatio-temporal dependence structure that can be estimated by borrowing strength from neighbouring regions and all years.  ...  For this purpose, we use the local similarity of temporal patterns by developing a spatial clustering model based on Bayesian nonparametric smoothing techniques.  ...  Wavelet coefficient at position m of resolution l, for kth covariate in rth cluster g rk (lm) Appendix Bernoulli random variable for the spike-and-slab prior: 0 means b rk (lm) is a point mass at 0,  ... 
doi:10.2478/jos-2021-0028 fatcat:5ozf45wxc5gsrgtlg27rqjrp5u

Bayesian Joint Modeling of Multiple Brain Functional Networks [article]

Joshua Lukemire, Suprateek Kundu, Giuseppe Pagnoni, Ying Guo
2019 arXiv   pre-print
Conditional on these edge probabilities, connection strengths are modeled under a Bayesian spike and slab prior on the off-diagonal elements of the inverse covariance matrix.  ...  The proposed Bayesian Joint Network Learning approach develops flexible priors on the edge probabilities involving a common intrinsic baseline structure and differential effects specific to individual  ...  world and scale-free networks simulation scenarios, and additional details on the Stroop Task data analysis.  ... 
arXiv:1708.02123v2 fatcat:g54vkaxhhnbfhp2yqcwyj2chte

Semiparametric Functional Factor Models with Bayesian Rank Selection [article]

Daniel R. Kowal, Antonio Canale
2022 arXiv   pre-print
The nonparametric factors are regularized with an ordered spike-and-slab prior that provides consistent rank selection and satisfies several appealing theoretical properties.  ...  inference on the effective number of nonparametric terms--all with minimal additional computational costs.  ...  Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.  ... 
arXiv:2108.02151v3 fatcat:qtr24igr5bhd5jwqfpd4763k3m
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